The Structure of the Young Symmetrizers for Spin Representations of the Symmetric Group, I

This paper is the first in a series of three papers on the Young symmetrizers for the spin representations of the symmetric group. In this opening paper, it is shown that the projective analogue of the Young symmetrizer recently introduced by Nazarov has a structure resembling thepλqλ-form exhibited by the classical symmetrizer. In contrast to the classical case, our decomposition of the projective symmetrizer requires an additional intermediate factorxλ. This factor will be studied in greater detail in the later papers.